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Noncausal solution, Lorentz Geometry, and trying a LaGrangian solution to deriving inertia

December 31, 2012

Happy New Year with wishes for peace and prosperity to all!

I had worked out the group wave concept for explaining non-causal quantum interactions, and realized how logical it seems–we are so used to thinking about the speed of light limit causing causal behavior that it makes the non-causal quantum interactions seem mysterious.  But when thinking of a universe that spontaneously developed from nothing, non-causal (infinite speed) interactions should be the default, what is weird is why particles and fields are restricted to the speed of light.  That’s why I came up with the group wave construct for entities–a Fourier composition of infinite speed waves explains instant quantum interference, but to get an entity such as a particle to move, there is a restriction on how fast the wave can change phase.  Where does that limitation come from?  Don’t know at this point, but with that limitation, the non-causal paradox is resolved.

Another unrelated realization occurred to me when I saw some derivation work that made the common unit setting of c to 1.  This is legal, and simplifies viewing derivations since relativistic interactions now do not have c carried around everywhere.  For example, beta in the Lorentz transforms now becomes Sqrt(1 – v^2) rather than Sqrt(1 – (v^2/c^2)).  As long as the units match, there’s no harm in doing this from a derivation standpoint, you’ll still get right answers–but I realized that doing so will hide the geometry of Lorentz transforms.  Any loop undergoing a relativistic transform to another frame of reference will transform by Sqrt(1 – (v^2/c^2)) by geometry, but a researcher would maybe miss this if they saw the transform as Sqrt(1 – v^2).   You can see the geometry if you assume an electron is a ring with orientation of the ring axis in the direction of travel.  The ring becomes a cylindrical spiral–unroll one cycle of the spiral and the pythagorean relation Sqrt(1 – v^2/c^2)) will appear.  I was able to show this is true for any orientation, and hand-waved my way to generalizing to any closed loop other than a ring.  The Lorentz transforms have a geometrical basis if (and that’s a big if that forms the basis of my unitary twist field theory) particles have a loop structure.

Then I started in on trying to derive general relativity.  Ha Ha, you are all laughing–hey, The Impossible Dream is my theme song!  But anyway, here’s what I am doing–if particles can be represented by loops, then there should be an explanation for the inertial behavior of such loops (totally ignoring the Higgs particle and the Standard Model for right now).  I see a way to derive the inertial behavior of a particle where a potential field has been applied.  A loop will have a path through the potential field that will get distorted.  The energy of the distortion will induce a corrective effect that is likely to be proportional to the momentum of the particle.  If  I can show this to be true, then I will have derived the inertial behavior of the particle from the main principle of the unitary twist field theory.

My first approach was to attempt a Lagrangian mechanics solution.  Lagrange’s equation takes the difference of the kinetic energy from the potential energy and creates a time and space dependent differential equation that can be solved for the time dependent motion of the particle.  It works for single body problems quickly and easily, but this is a multiple body problem with electrostatic and magnetic forces.  My limited computation skills rapidly showed an unworkable equation for solution.  Now I’m chewing on what simplifications could be done that would allow determining the acceleration of the particle from the applied potential.

Agemoz

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Noncausal interactions in the Unitary Twist Field Theory

December 10, 2012

It’s been a little while since I’ve posted, partly because of my time spent on the completion of a big work project, and partly because of a great deal of thinking before posting again (what a concept!  Something new!).  This blog has traveled through a lot of permutations and implications of the unitary twist field theory.  It starts by assuming that the Standard Model is valid, but then tries to create an underlying geometry for quantization and special relativity.  This twist vector field geometry is based on E=hv, and has worked pretty well–but when we get to entangled particles and other noncausal aspects of quantum theory, I’ve needed to do some new thinking.  While the noncausal construct is easily built on group wave theory (phase information propagates at infinite speed, but group Fourier compositions of waves that make up particles are limited to speed c), there are significant consequences for the theory regarding its view of the dimensional characteristics of the 3D+T construct of our existence.

As I mentioned, the unitary twist field theory starts with E=hv, the statement that every particle is quantized to an intrinsic frequency.  There really is only one way to do this in a continuous system in R3+T:  a twist within a background state vector field.  Twists are topologically stable, starting from the background direction and twisting to the same background direction with an integral turn.  Quantization is achieved because partial turns cannot exist (although virtual particles exist physically as partial turns for a short time before reverting back to the background state).  With this, I have taken many paths–efforts to verify this pet theory could really work.  For example, I tested the assumption of a continuous system–could the field actually be a lattice at some scale.  It cannot for a lot of reasons (and experiments appear to confirm this), especially since quantization scales with frequency, tough to do with a lattice of specific spacing.  Another concern to address with twist field theory occurs because it’s not a given that the frequency in E=hv has any physical interpretation–but quantum theory makes it clear that there is.  Suppose there was no real meaning to the frequency in E=hv–that is, the hv product give units that just happen to match that of frequency.  This can’t be true, because experimentally, all particles quantum interfere at the hvfrequency, an experimental behavior that confirms the physical nature of the frequency component.

So–many paths have been taken, many studies to test the validity of the unitary twist field theory, and within my limits of testing this hypothesis, it seems so far the only workable explanation for quantization.  I believe it doesn’t appear to contradict the Standard Model, and does seem to add a bit to it–an explanation for why we see quantization using a geometrical technique.  And, it has the big advantage of connecting special relativity to quantum mechanics–and I am seeing promising results for a path to get to general releativity.  A lot of work still going on there.

However, my mind has really taken a big chunk of effort toward a more difficult issue for the unitary twist field theory–the non-causality of entangled particles or quantum interference.  Once again, as discussed in previous posts here, the best explanation for this seems pretty straightforward–the particles in unitary twist field theory are twists that act as group waves.  The group wave cluster, a Fourier composition, is limited to light speed (see the wonderful discovery in a previous post that any confined twist system such as the unitarty twist field theory must geometrically exhibit a maximum speed, providing a geometrical reason for the speed of light limit).  However, the phase portion of the component waves is not limited to light speed and resolves the various non-causal dilemmas such as the two-slit experiment, entangled particles, etc, simply and logically without resorting to multiple histories or any of the other complicated attempts to mash noncausality into a causal R3+T construct.

But for me, there is a difficult devil in the details of making this really work.  Light-speed limited group waves with instantaneous phase propagation raises a very important issue.  Through a great deal of thinking, I believe I have shown myself that noncausal interactions which require instantaneous phase propagation, will specify that distance and time be what I call “emergent” concepts–they are not intrinsic to the construction of existence, but emerge–probably as part of the initial Big Bang expansion.  If so, the actual dimensions of space-time are also emergent–and must come from or are based on a system with neither–a zero dimensional dot of some sort of incredibly complex oscillation.  Why do I say this?  Because instantaneous phase propagation, such as entangled particle resolving, must have interactions in local neighborhoods that do not have either a space or time component.  Particles have two types of interactions–ones where two particles have similar values for R3+T (physical interactions), and those that have similar values only in phase space.  In either case, two particles will affect each other.  But how do you get interactions between two particles that aren’t in the same R3+T neighborhood?  Any clever scheme like the Standard Model or unitary twist field theory must answer this all important question.

Physicists are actively trying to get from the Standard Model to this issue (it’s a permutation of the effort to create a quantum gravity theory).  As you would expect, I am trying to get from the unitary twist field theory to this issue.  Standard Model efforts have typically either focused on adding dimensions (multiple histories/dimensions/string theories) or more exotic methods usually making some set of superluminal assumptions.  As mentioned in previous posts, unitary twist field theory has twists that turn about axes in both an R3 and a direction I that is orthogonal to R3 in time.  Note that this I direction does not have any dimensional length–it is simply a vector direction that does not lie in R3.  When I use the unitary twist field theory to show how particles will interact in R3+T, either physically or in entangled or interfering states, those particles would simply have group wave constructs with either a matching set of R3+T values (within some neighborhood epsilon value) or must have matching phase information in the I space.  In other words, normal “nearby”  interactions between two particles happen in a spacetime neighborhood, but quantum interference interactions happen in the I space, the land that Time and Space forgot.  There is no dimensional length here, but phase matches allow interaction as well.  This appears to be a fairly clean way to integrate noncausal behavior into the unitary twist field theory.

Obviously, there are still things to figure out here, but that is currently the most promising path I see for how unitary twist field theory will address the noncausal interaction construct issue.

Agemoz

 

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Symmetry Constraint on Charged Particle Geometry

June 5, 2012

In working out the details of how the complex unitary twist field would work on a system of two charged particles, I came across a very important discovery.  This holds true even if you don’t believe in the unitary twist field theory tooth fairy, even if you only think in terms of QFT virtual particles.

If you have two identical charged particles such as electrons separated by a distance r, symmetry geometry requires that the interaction cannot be static.  Any continuous static field in this system must have a plane perpendicular to the path between the particles that is the same as if there were no particles–that is, identical to the background field.  For standard QFT, this plane cannot have an electrostatic potential relative to the field out at infinity.  For the Complex Unitary Twist Field theory, this plane must be at the background field state in the imaginary dimension.

 

But if this is true, then that becomes a point where the behavior of one particle cannot affect the other–there is no field potential.  I won’t go into the QFT case, but the analogy is similar when I try to work a geometric solution in the twist field case.  I had found a way that the bend of the twist field imaginary background vector would specify the effect of charge on the second particle.  But this bend has to be symmetric in this system, with a plane in the middle where the bend is the same as the overall background field with no charges.  Oops–the problem shows up where there is no way to communicate the bend effect to the second particle without creating a paradox–an impossible field situation.

 

Any static field between two identical charged particles must have a plane between them that cannot pass the charge effect. The charge effect must pass dynamically across this plane

I said, uh-oh–the unitary twist field can’t work this way with bends.  Then I realized this has to be true for QFT too!  The symmetry of the system says that there is no way that the charged particle force can be conveyed within a static field.  There has to be something dynamic passing through the plane–virtual photons for QFT, and probably some type of background vector motion for the unitary twist field.  These two theories have to converge, and symmetry is going to severely constrain what has to be happening across the plane.  Even if you ignore unitary twist field theory, and just make the statement that QFT claims that virtual photons are not real (and unitary twist field theory specifies virtual photons as partial field twists that don’t complete but revert back to the background vector state), this symmetry problem forces the virtual photons to have both a physical field property and a property of motion.

Agemoz

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Vector Field Neighbors

May 28, 2012

I have been thinking a lot about the latest work on twist fields.  It has a lot of good things about it, it appears to successfully add quantization and special relativity to a vector field.  It opens up a possible geometry for the particle zoo.

But if this is really going to be workable or provable, I’m going to have to create a simulation, and that has to start with a mathematical basis.  And that wont come until I understand how the vector field operates on neighbors.  Yes, the unitary twist field has the right configuration to make things work, but the actual quantitative behavior is completely dependent on how the field propagates in space and time.  Up to now, the model looks like a sea of rotating balls, each with a black point spot that normally points in an imaginary direction, but can temporarily point in a real space formed by three real basis vectors orthogonal to the imaginary direction.  (Note that this discrete representation simplifies visualization, but there is no reason that the correct solution can’t be continuous, in fact I suspect it is).  If there is a connection between adjacent ball directions, the necessary quantization, stable particle formation, and special relativity behaviors will result.  However, a quantitative specification of these behaviors is entirely and completely specified by the nature of this neighborhood connection.

How does one ball affect its immediate neighbors?  Can a ball affect nearby balls that are not immediate neighbors?  Can a ball move in 3D or is everything that happens solely a function of ball rotation in place?  I see only two possible connections, one I call gear drive (a twist motion induces an adjacent ball in the twist plane to twist in the same (or opposite) direction) and the other I call vortex drive (a ball twist causes an adjacent ball on the twist axis to turn in the same or opposite direction).  Both of these forces could also induce normal twists, for four possible neighbor connections.  Which, or what set, of these neighbor interactions are valid descriptions of how balls move?  And what mathematically is the exact amount of dispersion of twist to neighbors?  Is the field continuous or can discontinuities occur?

Certainly the requirement for continuity is a powerful constraint, allowing discontinuities from the imaginary to any of the real axes, but prohibiting discontinuities between the real axes or in the imaginary direction.

These are the questions I have been pondering a lot.  I have come up with a nice framework but now I have to work out just how the vector field neighbor connection must happen before I make any further progress.

Agemoz

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Fine Structure Constant Hunting

May 1, 2012

Built into current QED (quantum electrodynamics) is the QFT process of pertubative accumulation of virtual photons.  Each possible virtual photon term is assigned a unitless  probability (actually,  probability amplitude capable of interfering with other terms)  of occurrence called the fine structure constant.   Searching for the reason for the value of this constant is a legendary pursuit for physicists, Feynman made the famous comment about it:

It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.

All kinds of research, study, and guesses have gone into trying to figure out why this number is what it is, and I can guarantee you this is a fruitless pursuit.  Think about it, there have been maybe millions of physicists over the last 100 years, the vast majority with IQs well north of 150, all putting varying amounts of effort into trying to figure out where this number comes from.  If none of them have come up with the answer yet, which they haven’t, the odds of you or I stumbling across it is certifiably close to zero.  That is an effort that I consider a waste of time. For one thing, this is a no-numerology physics blog.

One bad trait of many amateur physicists is to theorize answers by mixing up various constants such as pi, e, square roots, etc, etc and miraculously come up with numbers that explain everything.  Note, no knowledge required of the underlying science–just mix up numbers until something miraculous happens, you get a match to an actual observed physical constant (well, so close, anyway, and future work will explain the discrepancy.  Yeah… riiiight).  Then you go out and proselytize your Nobel prize winning theory, to the annoyance of everyone that sees what you did.  This is also called Easter egg hunting, and really is a waste of time.  Don’t do that.  Hopefully you will never ever see me do that.

Nevertheless, physicists are desperate for reasons why the fine structure constant is what it is, and all kinds of thought, analysis, and yes, numerology, have already gone into trying to find where it comes from.  Why do I insert a post about it in the midst of my step by step procedure of working out the role of unitary twist field theory in the electron-photon interaction?  Because, as I mentioned, the fine structure constant is fundamental to mathematically iterating terms in the QFT solution to this particular QED problem.  It stands to reason that an underlying theory would have a lot to say about why the fine structure constant is what it is.

Unfortunately, it’s clear to me that it’s not going to be that simple.  Pertubative QFT is exactly analogous to the term factors in a Taylor series.  You can create amazing functions from a polynomial with the right coefficients–I remember when I was much younger being totally amazed that you could create trigonometric functions from a simple sum of factors.  Just looking at the coefficients really tells you very little about what function is going to result, and that is exactly true in pertubative QFT.  The fine structure constant is your coefficient multiplier, but what we don’t have is the actual analytic function.  The fine structure constant has a large number of ways to appear in interaction computation, but the direct connection to real physics is really somewhat abstract.  For example, suppose I could geometrically explain the ratio of the charge potential energy between two electrons separated by distance d with the energy of a photon who’s energy is defined by that same distance d, which is defined as the fine structure constant value.  But I can’t.  The fact that it takes 137 of these photons (or equivalantly a photon with 1/137 the distance) to hold together two electrons to the same distance is not physically or geometrically interesting, it is a numerology thing.  Pursuing geometric reasons for the 137 is a lost cause, because the fine structure constant is a coefficient multiplier, an artifact of pertubative construction.

Nevertheless, I do see a way that the fine structure constant might be derived from the unitary twist field theory.  Don’t hold your breath–obviously a low IQ type like me isn’t likely to come up with any real discovery here.  Even so, I should follow through.  Here’s the deal.  Take that picture in the previous post, the second “Figure 2” that shows the effect of bending the imaginary vector.  I need to go back and edit that diagram, the circle ring is the twist ring electron, and fix that to be fig 3.  Anyway, the force on that electron ring is going to be determined by one of two things–the amount of the bend or the difference delta of the bend on one side of the ring versus the other.  The bend will gradually straighten out the further you get from a remote charge.   This computation will give the motion and hence the inertia of any self-contained twist (only the linear twist, the photon, will experience no net force from an imaginary bend).  This will be a difficult computation to do directly–but remember we must have gauge invariance, which leads to my discovery that a ring with an imaginary bend must have a frame of reference with no bend.  Find this frame of reference, and you’ve found the motion of the electron ring in the first frame of reference–a much easier computation to do.  This is real analysis and logical thinking, I think–not Easter egg hunting.

Agemoz

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Unitary Twist Field Dreams

April 12, 2012

I’m going to do something a little different in this post.  It’s every amateur’s dream to be taken seriously by the professionals, so I’m going to have a little fun today and pretend that a physics professor looked at this and decided to be nice (he just got a big grant approved for his research and was feeling unusually magnanimous) and go over it with me.  This is not for real–a real professor would almost certainly not give the time of day to an amateur’s ideas–it just is too much work to dig in and be precise about why any set of ideas wont work, nevermind those from someone who hasn’t spent a lifetime dedicated to this field of study.  But, amateurs all get their Walter Mitty dreams, and this is mine–and this is my blog, so I can do what I durn please here!  Actually I don’t care if I’m recognized for anything I come up with, but it’d be cool if some part of it turned out to be right.  Anyway, here goes.

Prof Jones:  Hello, what do you have for me?

Me:  I have this set of ideas about how particles form from a field.

Prof Jones:  You have a theory [suppresses noisy internal bout of indigestion]

Me:  Well, yes.  I think there is a geometrical basis for quantum and special relativistic behavior of particles.

Prof Jones:  We already have that in QFT.  Are you adding or revising existing knowledge?  I’m really not interested in someone telling me Einstein or anybody else was wrong…

Me:  I believe I am adding.  I have tried to take a overall high-level view of what is now known, especially the E=hv relation and the special relativity Lorentz transforms, and see some conclusions that make sense to me

Prof Jones:  Well, I’ve had a lot of ideas thrown at me, and they are a dime-a-dozen.  It’s not the idea that’s important but the logic or experiment that supports it.  A good theory explains something we don’t understand and allows us to successfully predict new things we otherwise would not find.  Is yours a good theory?  Do you have supporting evidence or experiment?  Can you predict something I don’t already know with QFT?  Does it contradict anything I already know?  If you can’t pass this complete criteria, the theory isn’t going anywhere but the round file.

Me:  I don’t have anything that proves it.  I don’t have anything it predicts right now but I see some possibilities.  I don’t think it contradicts anything, but there are some question marks.

Prof Jones:  Urrg…. Well, this is your lucky day.  I happen to be in the mood for shooting down the bright ideas of poor suckers that think Nobel prizes are given out like puppies from a puppy mill to people that haven’t paid their dues in this very, very tough field.  So, let’s start with this question:  What makes you think you are the one that has come up with something new in quantum theory?  After all, you can’t argue that the set of smart-enough people that actually can legitimately call themselves physicists, theoretical or related, have spent cumulative millions of lifetimes trying to break down the data and clues we have to solve the very well-known problem you are looking at.  Don’t you think someone, or many someones, with a much deeper background than you would have long since considered whatever you have and passed it by fairly quickly?

Me:  [meekly] yes.

Me:  But I have thought about this for a very long time, and refined it, and received feedback, and really tried hard to make sure it makes sense.

Prof Jones:  Unfortunately, so has every honest physics PhD, and I’m afraid they are going to have a lot more mental “hardware” than you, having both genuine talent and also having brutally difficult training in abstract mental comprehension and synthesis ability and current knowledge.

Me: OK.  I guess I could quit doing this–I just find it so interesting.

Prof Jones: [softens just slightly, realizing there’s a lot of snarky but not-classy power in putting down those who try, but are so limited in resources or study time].  Well, just so you understand.  You aren’t going anywhere with this.  But let’s see what you got.  Before I dig in, I want to know what you are adding to existing theory, as succinctly as you can communicate.

Me:  Alright.  I thought about the way quantization works on particles and fields, and in both cases the E=hv relation defines very explicitly what must happen.  I spent a lot of time trying to construct a model of a system that is continuous but obeys this relation at the smallest scale.  I came up with three constraints that describe such a system–in fact, it looks to me that the E=hv relation actually specifies a geometrically defined system.  These constraints are:

1: The quantization is enforced by a rotation in a vector field, that is, a twist.

2: To ensure that only single complete rotations can occur, the field must have a local background state that the rotation returns to.

3: To ensure that the energy of the rotation cannot dissipate, the vector field must be unitary.  Every field element must have constant magnitude but can rotate in 3D+T spacetime.

Prof Jones:  I see what you are getting at.  The E=hv relation only allows discrete energy states for a given frequency within an available continuous energy range.  A twist is a modulus operation that works in a continuous 3D field to provide such discrete states provided that there is a default idle state, which would be your background vector orientation.  However, you realize that EM fields do not have limitations on magnitude, nor is there any evidence of a background state.

Me: I understand that.  I am proposing that because QFT shows how EM fields can be derived from quantum particles (photons), my theory would underlie EM fields.  I see a path where EM fields can be constructed from this Unitary Twist Field Theory from sets of quantized twists.  I agree that the background vector direction is a danger because it implies an asymmetry that could prevent gauge invariance–but I suspect that any detector built of particles that are formed from this twist mechanism cannot detect the background state.  The background state direction doesn’t have to be absolute, it can vary, and a unitary vector field has to point somewhere.  Continuity and energy conservation imply that local neighborhoods would point in the same direction.

Prof Jones:  Sets of quantized twists, hunh.  Well, you’ve got a very big problem with that idea, because you cannot construct a twist in a background unitary vector field without introducing discontinuities.  If you have discontinuities, you don’t have a unitary vector field.

Me: Yes, I agree.  However, if the twist moves at speed c, it turns out the discontinuities lie on the light cones of each point in the twist and are stable, each light cone path has a stable unchanging angle.  In a sense, travelling at the speed of light isolates the twist elements from what would be a discontinuity in a static representation.

Prof Jones:  I don’t think I agree with that, I would have to see proof.  But another question comes to mind.  In fact a million objections come to mind but let me ask you this.  You are constructing an EM field from this unitary vector field.  But just how does this single vector field construct the two degrees of freedom in an EM field, namely electrostatic fields and magnetic fields?  Just how are you proposing to construct charge attraction and repulsion and magnetic field velocity effects specified by Maxwell’s relations?  QFT is built on virtual particles, in the EM case, virtual photons.  How are you going to make that work with your theory?  You realize the magnitude, don’t you, of what you are taking on?

Me:  These are questions I have spent a great deal of time with over the last 20 years.  That doesn’t justify a bad theory, I know.  So I’ll just present what I have, and if this dies, it dies.  I’d just like to know if my thinking has any possible connection to the truth, the way things really are.  I realize that we have a perfectly workable theory in QFT that has done amazingly well.  But we also have a lot of particles and a lot of interactions that seem to me to have an underlying basis that QFT or relativity don’t explain, they just happen to work.  Renormalization works, but why?  These are some issues that tell me we can’t stop with QFT.

Prof Jones:  [sotto voce] The hubris is strong in this one.

Me: What

Prof Jones:  Nothing.  Go on.  What is your theory going to do with charge and magnetic behavior?

TO BE CONTINUED, SAME BAT-TIME, SAME BAT-CHANNEL

Agemoz

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Twist Theory and Electrons

April 6, 2012

OK, applying this unitary twist field idea to photons seems pretty workable.  We get real photons and virtual photons, and get a good model for how quantization and circular polarization could work.

There are some big questions, though–the biggest of all is that this method of quantizing a continuous system requires a background vector state.  Now, this isn’t as bad as it would seem, because a unitary vector field has to have some direction, and continuity would imply that local neighborhoods would point in the same direction, and the model does not assume that the backround direction has to be absolute throughout, it can change.  Nevertheless, it would seem that a background direction might somehow be detectable with some variation of a Michelson-Morley experiment.  That’s going to get some attention on my part later, but for now I want to go in another direction.

Let’s talk electron models in the Twist Theory.  This is where real physicists have a heyday killing off new theories like this because the electron is so well studied and measured, there is so much that a theory would have to line up with before even beginning to come up with something new.  Don’t know what to say except it’s fun to see what comes out of such a study.

Let’s start with degrees of freedom, just like I just did with the photon, that could kill off the theory in a hurry–and for a long time I knew there was a problem, here it is:  electrons come in four permutations, spin up electron, spin-down electron, spin-up positron, and spin-down positron.  All of these have the same exact mass, charge (+ or -), spin moment, g ratio, and so on.  I have long felt that the electron is effectively modeled with a single unitary field twist ring.   Here’s a picture of the idea.

Twist ring model of an electron in a unitary field with a background state.

The ring has one point where the twist direction matches the background twist state.  The twist curves, unlike the photon, due to internal effects of the ring twist.  I have done math that shows there is a single such solution that is stable, but only in certain circumstances.  I will come back to the math of twist ring solutions, but right now, let’s just see if the degrees of freedom required would shoot this down even before getting to the math.  Sort of like checking to make sure an equation has consistency of units, otherwise the equation is just nonsense.  As I mentioned, there are four variations of the electron that have to have a unique twist field representation.  Are there four unique solutions for the twist ring?

Twist ring degrees of freedom with no background state. Note that two solutions are just mirror images of the other two, we only have one degree of freedom.

Of course, we have our four cases, and no more.  Ooops–wait, two of the four are just mirror images of the first two–we really only have two unique twist ring solutions!  It took me a while to realize there are actually four–in a unitary twist field there would only be two, but in a unitary twist field with a background state, necessary for quantization to work, there are actually four.

The background state required for quantization also provides a reference that prevents the two mirror cases from being identical to the first two cases. There are now two degrees of freedom.

The background state from which the twist must begin acts as a reference vector that keeps the mirror image twist rings from being identical by rotation.  To see this more clearly, look at the two degrees of freedom as a function of the planes they reside in:

The reference vector along with the ring center defines a plane (green) where two possible twist cases result in a unique degree of freedom. The blue plane that the ring resides in defines ring travel direction and is another unique degree of freedom.

One degree of freedom is establised by the ring rotation within the plane that includes the ring.  There are two possibilities, clockwise or counterclockwise.  The second degree of freedom is defined with the plane that the background vector lies in, as well as the center of the twist ring.  The background vector is the starting point for a rotation about the ring circumference.  It should be clear that the background vector creates a reference that makes the two mirror cases unique.  You could argue that it doesn’t matter if the mirror image rotation doesn’t have the same background state, but actually it does–it determines which way the ring will turn if it is moving in a magnetic field–the spin-up electron will move differently than the spin-down electron due to the opposite direction of its starting point vector.  I’ll keep thinking about this but so far, this appears to be valid.

Agemoz

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Twist discontinuity and Strings

December 15, 2011

As I’ve worked through figuring out what a mathematical description of a twist with a discontinuity would look like, I found several fascinating results.  First, I realized that the sheath surface surrounding the twist would have to be as thin as possible, a long tube of epsilon width–otherwise there would be paths outside of the twist that would get pushed aside, causing potential variations.  The lowest energy state for the twist with a sheath would have to be essentially one dimensional, tied down to the background state on either end.  Oh ho, I thought–this looks an awful lot like a string!

I’ve never been a fan of string theory–not because of the model that uses strings, but because string theory is associated with rolled up extra dimensions.  I’ve felt that adding rolled up dimensions, or any form of dimensional structure hidden within our three spatial dimensions, is a deus ex machina device to cram general relativity math into QFT.  In addition, I have the more subjective view that nature finds a way–if there were other dimensions, nature would fill it with vermin that evolved to take advantage of the space.  We would observe non-conservation of mass in the dimensions we can’t see in that case.  Of course, that is no proof, but it’s my instinct that if there really were something we would call a dimension orthogonal to our R3 space, our rules of conservation wouldn’t always hold.

So, the irony is that when I allow discontinuities into my twist field theory, I see that strings have to result or the theory can’t work.  This does several things–first, the problem of photon circular polarization becomes trivial.  Second, this matches the theory premise that twists have to have a tiny width, if any.  More of why this is so can be seen in my Paradoxes paper (rather old, and getting out of date as I’ve done further research–but the basic ideas still seem to work).

But where the string model gets *really* interesting is the realization that the twist enclosed with an infinitesimally thin sheath only has one path.

Quantum Field Theory works extraordinarily well, by that I mean that doing perturbative summations of multiple paths yields extremely accurate results confirmed by experiment.  So why is there no term for an electron interacting with an electron, or a photon interacting with a photon.  You thought that the infinities to be renormalized were bad before, wait till you throw those stinkers into the mix!   It’s because those two items consist of only one path.  That is why they have fixed particle parameters that don’t vary regardless of what is nearby–they are atomic, to use a rather ironic term.  An electron can interact with another electron only via photons, there is no way to some how break down an electron so it will interact directly with another–same with a photon.  There is only one path for each.  And this twist field string, with a sheath discontinuity, provides the reason why.

If it is right.

Agemoz

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Twist ring simulation pictures

May 22, 2009

That was a really exciting insight about twist rings! To prove that I wasn’t just being stupid, or at least less crackpotty than most wannabes, here are some simulation pictures of the twist ring model. Notice how it is stable and has the same radius regardless of a variety of particle initial conditions. It sometimes oscillates as it approaches the ring state but always locks into the final ring. This was an incredibly important outcome for my study–because if you model a ring with electrostatic forces and momentum, you do *not* get a stable ring–you get ellipses and other shapes depending on the initial conditions, and perturbations are not restoring. The 1/r^3-1/r^2 model using both electrostatic and magnetic forces is the first geometrical ring model that I have found that is stable and self-restoring.

Here is a magnified view, it’s a little easier to see the ring here

Some more initial conditions, but all settle into the stable ring state.

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twist ring unique diameter and potential solution

May 15, 2009

Well, you’ll have to bear with me–I am spending a lot of time with twist rings because there’s so much potential for representing real particles, and I just recently had a remarkable insight! The original work I did on charge loops petered out because it ran into problems explaining multi-particle interactions, and it wasn’t possible to model the four electron types (spin-up electron, spin-down electron, spin-up positron, spin-down positron). The twist ring works in both of these situations, and brings a lot more to the table–such as explaining why photons are quantized without limiting possible frequencies (integral number of twists required).

I had been concerned with any ring model of the electron because I could not see how a scale-less system could produce a particle with a constant energy/wave frequency as a ring–but now I see a possibility, one that also has the potential to derive the particle displacement response to a force. This, of course, means that twist rings have a way of having inertial properties–that is, mass.

But, let’s look at the radius of a ring. Charge loops and twist rings both have the experimental problem of not being the point kernels we see in accelerator experiments. It should be obvious that a point kernel is not possible under the Heisenberg Uncertainty relation, but Standard Model physicists do not consider that a fatal objection, just something we don’t understand yet. The only way I can see any ring solution being acceptable is if rings distort to narrow ovals as they are accelerated (and interestingly enough, using the semiclassical Compton radius in such a situation results in a ring that exactly obeys the Heisenberg relation Dx * Dy = h). As the particle approaches the speed of light, the ring becomes almost a straight line and thus could look like a point without violating the Heisenberg relation (in fact, could explain why the Heisenberg relation is true!).

Nevertheless, there is another problem with any ring solution that goes beyond why do experiments seem to show point sources for electrons: If it is a ring, why do electrons only have one possible radius? Why are there no stable particles that have 1.1 times the mass of an electron just by decreasing the ring wave frequency a bit and increasing the ring radius a bit? Valid stable rings of any diameter should be possible if we look at twist rings as systems of single cycle standing waves, where there are momentum (centripetal) and electrostatic forces in balance.

I suddenly realized that I had been assuming a momentum element that, in the case of a twist ring model, isn’t a valid assumption–nowhere in that model is there a means of expressing momentum. I could fell two birds with one stone if I got rid of that assumption, because it turns out that twist rings do have counter-balancing forces without need for momentum, and this has the potential of then deriving the particle momentum and hence its mass. Unlike charge loops, twist rings have intra-particle electrostatic *and* magnetic forces at play, and they counteract each other in a stable way, it is not metastable: Since magnetic forces drop off as 1/r^3, and electrostatic forces drop off as 1/r^2, there are two extremely important results that not only guarantee that there is only one stable radius, but it guarantees that a twist ring that gets a little too big has a correcting attractive force to reduce its size, and a particle that gets a little too small gets a correcting repulsive force that lets the particle ring get a little bigger. Take a look, it’s fascinating–if the radius gets bigger, the 1/r^2 term, which is the attractive electrostatic force, predominates over the 1/r^3 term, but when the radius gets smaller, the repulsive magnetic force that goes as 1/r^3 predominates over the 1/r^2. The twist ring has one fixed radius set by opposing electrostatic and magnetic forces, and it is self-correcting. The twist ring could be the solution that gives us the God frequency (mass of the electron). I should now be able to use the behavior of a twist ring in an electric (or magnetic field) to derive the inertial response using F = Eq = ma, and from there derive the mass and momentum of the particle.

Wow. I have to think about that for a while. I bet there is not one single person in the universe that believes what I said has truth to it! I’m not even sure I do either, but it’s an astonishing revelation!

Agemoz

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